Finite Group Databasebeta

← C4×#99×D71 #31995096

Subgroups — C4×#99×D71 #31995096

Order 18176.

2242 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D71C211yesmaximal, characteristic
2C2×#99×D71C212yesmaximal
3C4×C22⋊C4×D71C212yesmaximal, complemented
4#99×Dic71C212yesmaximal, complemented
5C4×#14556042C212yesmaximal, complemented
6C4×#14556043C211yesmaximal, characteristic, complemented
7#22588127C212yesmaximal, complemented
8#342×D71C212yesmaximal, complemented
9C4×#99×C71C211yesmaximal, characteristic, complemented
10C22×D4×D71C2211yescharacteristic
11C23×C4×D71C411yescharacteristic, complemented
12C23×C4×D71C2211yescharacteristic
13C2×C4×D284C411yescharacteristic, complemented
14C2×D4×Dic71C2211yescharacteristic
15C2×#14556090C411yescharacteristic, complemented
16C2×C4×C22⋊D71C411yescharacteristic, complemented
17C2×C4×C22⋊D71C2211yescharacteristic
18C2×(C22⋊D71)⋊C4C411yescharacteristic, complemented
19C2×(C22⋊D71)⋊C4C2211yescharacteristic
20C4×D4×D71—22no—
21C4×D4×D71—22no—
22C4×D4×D71—22no—
23C4×D4×D71—22no—
24C2×C4⋊C4×D71C411yescharacteristic, complemented
25C2×C22⋊C4×D71C411yescharacteristic, complemented
26C2×C22⋊C4×D71C2214yes—
27C2×C22⋊C4×D71C2211yescharacteristic
28C2×C42×D71—22no—
29C2×C42×D71C411yescharacteristic, complemented
30C2×#14556043C2212yes—
31C2×#14556042C2214yes—
32#99×D71C4116yesdirect product factor
33C22⋊C4×Dic71C2214yescomplemented
34C4×(C2×D71)⋊C4—22no—
35C4×C22⋊Dic71C2212yescomplemented
36#17985846—22no—
37#95×D71—22no—
38#17985766C2212yescomplemented
39#17985765C2214yescomplemented
40C2×C4×D4×C71C2211yescharacteristic
41C2×#99×C71C2212yes—
42C4×C22⋊C4×C71C2212yescomplemented
43#342×C71C2212yescomplemented
44C24×D71C2×C411yescharacteristic
45C24×D71C2311yescharacteristic
46C22×D284C2×C411yescharacteristic
47C22×C22⋊D71C2×C411yescharacteristic
48C22×C22⋊D71C2311yescharacteristic
49C2×D4×D71—22no—
50C2×D4×D71—22no—
51C2×D4×D71—24no—
52C2×D4×D71C2×C418yes—
53C23×Dic71C2×C411yescharacteristic, complemented
54C23×Dic71C2311yescharacteristic
55C22×C4×D71—24no—
56C22×C4×D71—21no—
57C22×C4×D71—21no—
58C22×C4×D71—21no—
59C22×C4×D71—21no—
60C22×C4×D71—44no—
61C22×C4×D71—44no—
62C22×C4×D71C2×C411yescharacteristic
63C22×C4×D71C2×C411yescharacteristic
64C22×C4×D71C2×C411yescharacteristic
65C22×C4×D71C2×C411yescharacteristic
66C22×C4×D71C2×C411yescharacteristic
67C22×C4×D71C2×C411yescharacteristic
68C22×C4×D71C2×C411yescharacteristic
69C22×C4×D71C2×C411yescharacteristic, complemented
70C22×C4×D71C2×C411yescharacteristic, complemented
71C22×C4×D71D412yes—
72C22×C4×D71D412yes—
73C22×C4×D71D412yes—
74C22×C4×D71D412yes—
75C4×D284—22no—
76C4×D284—22no—
77D4×Dic71—22no—
78D4×Dic71—22no—
79#14556090—22no—
80#14556090—22no—
81C4×C22⋊D71—22no—
82C4×C22⋊D71—22no—
83C4×C22⋊D71—22no—
84C4×C22⋊D71—22no—
85(C22⋊D71)⋊C4—22no—
86(C22⋊D71)⋊C4—22no—
87(C22⋊D71)⋊C4—22no—
88(C22⋊D71)⋊C4—22no—
89C2×C4⋊Dic71C2×C411yescharacteristic, complemented
90C2×Dic71⋊C4C2×C411yescharacteristic, complemented
91C2×Dic71⋊C4C2×C411yescharacteristic, complemented
92C4⋊C4×D71—22no—
93C4⋊C4×D71—22no—
94C2×C22⋊Dic71C2×C411yescharacteristic, complemented
95C2×C22⋊Dic71C2311yescharacteristic
96C2×C22⋊Dic71C2314yes—
97C2×(C2×D71)⋊C4—24no—
98C2×(C2×D71)⋊C4C2×C411yescharacteristic
99C2×(C2×D71)⋊C4C2×C411yescharacteristic
100C2×(C2×D71)⋊C4C2×C411yescharacteristic, complemented
101C2×(C2×D71)⋊C4C2×C411yescharacteristic, complemented
102C22⋊C4×D71—22no—
103C22⋊C4×D71—22no—
104C22⋊C4×D71—28no—
105C22⋊C4×D71—22no—
106C22⋊C4×D71—22no—
107C22⋊C4×D71C2×C4116yescomplemented
108C2×C4×Dic71—24no—
109C2×C4×Dic71—22no—
110C2×C4×Dic71C2×C411yescharacteristic, complemented
111C2×C4×Dic71C2×C411yescharacteristic, complemented
112C2×C4×Dic71C2×C411yescharacteristic, complemented
113C42×D71—21no—
114C42×D71—21no—
115C42×D71—21no—
116C42×D71—21no—
117C42×D71—48no—
118#14556043C2×C418yescomplemented
119#14556042C2×C4116yescomplemented
120C71⋊#95—24no—
121C71⋊#95—22no—
122C22×D4×C71C2311yescharacteristic
123C23×C4×C71C2×C411yescharacteristic, complemented
124C23×C4×C71C2311yescharacteristic
125C4×D4×C71—22no—
126C4×D4×C71—22no—
127C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
128C2×C22⋊C4×C71C2×C411yescharacteristic, complemented
129C2×C22⋊C4×C71C2311yescharacteristic
130C2×C22⋊C4×C71C2314yes—
131C2×C42×C71—22no—
132C2×C42×C71C2×C411yescharacteristic, complemented
133#99×C71C2×C418yescomplemented
134#95×C71—22no—
135C23×D71—21no—
136C23×D71—21no—
137C23×D71—22no—
138C23×D71—42no—
139C23×D71—42no—
140C23×D71—42no—
141C23×D71—42no—
142C23×D71C4214yescomplemented
143C23×D71C22×C411yescharacteristic
144C23×D71C22×C411yescharacteristic
145C23×D71C22×C411yescharacteristic
146C23×D71C22×C414yes—
147C23×D71C2×D412yes—
148C23×D71C2×D412yes—
149C23×D71#4114yes—
150C2×D284—22no—
151C2×D284—22no—
152C2×D284C4214yescomplemented
153C2×C22⋊D71—22no—
154C2×C22⋊D71—22no—
155C2×C22⋊D71—22no—
156C2×C22⋊D71—22no—
157C2×C22⋊D71C4214yescomplemented
158C2×C22⋊D71C22×C414yes—
159D4×D71—216no—
160D4×D71—216no—
161C22×Dic71—24no—
162C22×Dic71—21no—
163C22×Dic71—21no—
164C22×Dic71—42no—
165C22×Dic71—42no—
166C22×Dic71C22×C411yescharacteristic
167C22×Dic71C22×C411yescharacteristic
168C22×Dic71C22×C411yescharacteristic
169C22×Dic71C22×C411yescharacteristic
170C22×Dic71C22×C411yescharacteristic
171C22×Dic71C2×D412yes—
172C22×Dic71C2×D412yes—
173C2×C4×D71—21no—
174C2×C4×D71—21no—
175C2×C4×D71—22no—
176C2×C4×D71—24no—
177C2×C4×D71—28no—
178C2×C4×D71—21no—
179C2×C4×D71—21no—
180C2×C4×D71—21no—
181C2×C4×D71—21no—
182C2×C4×D71—216no—
183C2×C4×D71—21no—
184C2×C4×D71—21no—
185C2×C4×D71—21no—
186C2×C4×D71—21no—
187C2×C4×D71—42no—
188C2×C4×D71—44no—
189C2×C4×D71—42no—
190C2×C4×D71—44no—
191C2×C4×D71—42no—
192C2×C4×D71—44no—
193C2×C4×D71—44no—
194C2×C4×D71—44no—
195C2×C4×D71—44no—
196C2×C4×D71—48no—
197C2×C4×D71—48no—
198C2×C4×D71—44no—
199C2×C4×D71—42no—
200C2×C4×D71—42no—
201C2×C4×D71—42no—
202C2×C4×D71—42no—
203C2×C4×D71C4214yescomplemented
204C2×C4×D71C22⋊C411yescharacteristic
205C2×C4×D71C22⋊C411yescharacteristic
206C2×C4×D71C22⋊C411yescharacteristic
207C2×C4×D71C22⋊C412yes—
208C2×C4×D71C22⋊C412yes—
209C2×C4×D71C22⋊C412yes—
210C2×C4×D71C22⋊C412yes—
211C2×C4×D71C22⋊C412yes—
212C2×C4×D71C22⋊C412yes—
213C2×C4×D71C22⋊C411yescharacteristic
214C4⋊Dic71—22no—
215Dic71⋊C4—22no—
216Dic71⋊C4—22no—
217C22⋊Dic71—22no—
218C22⋊Dic71—24no—
219C22⋊Dic71—22no—
220C22⋊Dic71C22×C418yescomplemented
221(C2×D71)⋊C4—22no—
222(C2×D71)⋊C4—22no—
223(C2×D71)⋊C4—216no—
224(C2×D71)⋊C4—22no—
225(C2×D71)⋊C4—22no—
226C4×Dic71—21no—
227C4×Dic71—21no—
228C4×Dic71—21no—
229C4×Dic71—21no—
230C4×Dic71—21no—
231C4×Dic71—21no—
232C4×Dic71—48no—
233C4×Dic71—44no—
234C24×C71C22×C411yescharacteristic
235C24×C71C2411yescharacteristic
236C2×D4×C71—22no—
237C2×D4×C71—22no—
238C2×D4×C71C22×C414yes—
239C22×C4×C71—24no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—42no—
243C22×C4×C71—42no—
244C22×C4×C71C22×C411yescharacteristic
245C22×C4×C71C22×C411yescharacteristic
246C22×C4×C71C22×C411yescharacteristic
247C22×C4×C71C22×C411yescharacteristic
248C22×C4×C71C22×C411yescharacteristic
249C22×C4×C71C2×D412yes—
250C22×C4×C71C2×D412yes—
251C4⋊C4×C71—22no—
252C22⋊C4×C71—22no—
253C22⋊C4×C71—24no—
254C22⋊C4×C71—22no—
255C22⋊C4×C71C22×C418yescomplemented
256C42×C71—21no—
257C42×C71—21no—
258C42×C71—44no—
259C23×C71—21no—
260C23×C71—21no—
261C23×C71—41no—
262C23×C71—41no—
263C23×C71—41no—
264C23×C71—41no—
265C23×C71C2×C4212yescomplemented
266C23×C71C23×C411yescharacteristic
267C23×C71C23×C412yes—
268C23×C71C22×D412yes—
269C23×C71C2×#4112yes—
270C22×D71—24no—
271C22×D71—22no—
272C22×D71—24no—
273C22×D71—22no—
274C22×D71—21no—
275C22×D71—21no—
276C22×D71—24no—
277C22×D71—24no—
278C22×D71—48no—
279C22×D71—48no—
280C22×D71—41no—
281C22×D71—42no—
282C22×D71—41no—
283C22×D71—42no—
284C22×D71—42no—
285C22×D71—42no—
286C22×D71—48no—
287C22×D71—48no—
288C22×D71—42no—
289C22×D71—42no—
290C22×D71—41no—
291C22×D71—41no—
292C22×D71C2×C4212yes—
293C22×D71C2×C4212yes—
294C22×D71C2×C4212yescomplemented
295C22×D71C2×C22⋊C412yes—
296C22×D71C2×C22⋊C411yescharacteristic
297C22×D71C2×C22⋊C411yescharacteristic
298C22×D71#11712yes—
299C22×D71#11712yes—
300C22×D71C4×D418yes—
301C22×D71C4×D418yes—
302D4×C71—28no—
303C2×C4×C71—21no—
304C2×C4×C71—21no—
305C2×C4×C71—24no—
306C2×C4×C71—22no—
307C2×C4×C71—21no—
308C2×C4×C71—21no—
309C2×C4×C71—28no—
310C2×C4×C71—41no—
311C2×C4×C71—42no—
312C2×C4×C71—42no—
313C2×C4×C71—44no—
314C2×C4×C71—44no—
315C2×C4×C71—42no—
316C2×C4×C71—41no—
317C2×C4×C71—41no—
318C2×C4×C71C2×C4212yescomplemented
319C2×C4×C71C2×C22⋊C411yescharacteristic
320C2×C4×C71C2×C22⋊C412yes—
321C2×C4×C71C2×C22⋊C411yescharacteristic
322C22⋊D71—28no—
323C22⋊D71—28no—
324C2×Dic71—21no—
325C2×Dic71—21no—
326C2×Dic71—24no—
327C2×Dic71—22no—
328C2×Dic71—21no—
329C2×Dic71—21no—
330C2×Dic71—28no—
331C2×Dic71—41no—
332C2×Dic71—42no—
333C2×Dic71—42no—
334C2×Dic71—44no—
335C2×Dic71—44no—
336C2×Dic71—42no—
337C2×Dic71—41no—
338C2×Dic71—41no—
339C2×Dic71C2×C4212yescomplemented
340C2×Dic71C2×C22⋊C411yescharacteristic
341C2×Dic71C2×C22⋊C412yes—
342C2×Dic71C2×C22⋊C411yescharacteristic
343D284—28no—
344C4×D71—24no—
345C4×D71—24no—
346C4×D71—22no—
347C4×D71—24no—
348C4×D71—22no—
349C4×D71—24no—
350C4×D71—22no—
351C4×D71—24no—
352C4×D71—42no—
353C4×D71—42no—
354C4×D71—42no—
355C4×D71—42no—
356C4×D71—42no—
357C4×D71—432no—
358C4×D71—42no—
359C4×D71—42no—
360C4×D71—42no—
361C4×D71—42no—
362C4×D71—42no—
363C4×D71—42no—
364C4×D71#9914yesdirect product factor
365C22×C71—22no—
366C22×C71—21no—
367C22×C71—22no—
368C22×C71—21no—
369C22×C71—22no—
370C22×C71—42no—
371C22×C71—42no—
372C22×C71—42no—
373C22×C71—42no—
374C22×C71—41no—
375C22×C71—41no—
376C22×C71C22×C4211yescharacteristic
377C22×C71C22×C22⋊C411yescharacteristic
378C22×C71C2×#11711yescharacteristic
379C22×C71C2×C4×D414yes—
380C2×D71—21no—
381C2×D71—22no—
382C2×D71—21no—
383C2×D71—22no—
384C2×D71—216no—
385C2×D71—24no—
386C2×D71—24no—
387C2×D71—22no—
388C2×D71—42no—
389C2×D71—42no—
390C2×D71—48no—
391C2×D71—48no—
392C2×D71—42no—
393C2×D71—41no—
394C2×D71—41no—
395C2×D71—48no—
396C2×D71—42no—
397C2×D71C4×C22⋊C412yes—
398C2×D71C4×C22⋊C414yes—
399C2×D71C4×C22⋊C412yes—
400C2×D71C2×#9912yes—
401C2×D71#41012yes—
402C4×C71—21no—
403C4×C71—22no—
404C4×C71—22no—
405C4×C71—48no—
406C4×C71—41no—
407C4×C71—41no—
408C4×C71C2×#9912yescomplemented
409Dic71—21no—
410Dic71—22no—
411Dic71—22no—
412Dic71—48no—
413Dic71—41no—
414Dic71—41no—
415Dic71C2×#9912yescomplemented
416C2×C4×#99—711nomaximal, Sylow
417C2×C71—24no—
418C2×C71—21no—
419C2×C71—21no—
420C2×C71—42no—
421C2×C71C2×C4×C22⋊C411yescharacteristic
422C2×C71C22×#9911yescharacteristic
423C2×C71C2×#41011yescharacteristic
424D71—22no—
425D71—24no—
426D71—42no—
427D71C4×#9914yesdirect product factor
428C22×C4×D4—711no—
429C22×#99—712no—
430C2×C4×C22⋊C4—712no—
431C4×#99—712no—
432C4×#99—712no—
433C4×#99—712no—
434C4×#99—711no—
435C4×#99D7111yescharacteristic, direct product factor
436C2×#342—712no—
437C71C2×C4×#9911yescharacteristic, complemented, Sylow
438C23×D4—711no—
439C24×C4—711no—
440C24×C4—711no—
441C2×C4×D4—711no—
442C2×C4×D4—711no—
443C2×C4×D4—711no—
444C2×C4×D4—711no—
445C2×C4×D4—711no—
446C2×C4×D4—711no—
447C2×C4×D4—711no—
448C2×C4×D4—1422no—
449C2×C4×D4—1422no—
450C2×C4×D4—1422no—
451C2×C4×D4—1422no—
452C2×C4×D4C2×D7111yescharacteristic
453C22×C4⋊C4—711no—
454C22×C22⋊C4—714no—
455C22×C22⋊C4—711no—
456C22×C22⋊C4—711no—
457C22×C42—711no—
458C22×C42—1422no—
459C2×#99—712no—
460C2×#99—714no—
461C2×#99—7116no—
462C2×#99C2×D7112yes—
463C4×C22⋊C4—712no—
464C4×C22⋊C4—714no—
465C4×C22⋊C4—1422no—
466C4×C22⋊C4—1422no—
467C4×C22⋊C4C2×D7112yescomplemented
468C2×#95—1422no—
469#342—714no—
470#342—712no—
471#342C2×D7112yescomplemented
472C25—711no—
473C25—711no—
474C22×D4—711no—
475C22×D4—711no—
476C22×D4—718no—
477C22×D4—711no—
478C22×D4—1422no—
479C22×D4—1422no—
480C22×D4—1424no—
481C22×D4C22×D7111yescharacteristic
482C23×C4—2844no—
483C23×C4—2844no—
484C23×C4—711no—
485C23×C4—711no—
486C23×C4—711no—
487C23×C4—711no—
488C23×C4—712no—
489C23×C4—712no—
490C23×C4—712no—
491C23×C4—711no—
492C23×C4—711no—
493C23×C4—711no—
494C23×C4—711no—
495C23×C4—711no—
496C23×C4—711no—
497C23×C4—711no—
498C23×C4—712no—
499C23×C4—1421no—
500C23×C4—1421no—
501C23×C4—1421no—
502C23×C4—1421no—
503C23×C4—1424no—
504C23×C4C4×D7111yescharacteristic, complemented
505C23×C4C22×D7111yescharacteristic
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—1422no—
509C4×D4—1422no—
510C4×D4—1422no—
511C4×D4—1422no—
512C4×D4—1422no—
513C4×D4—1422no—
514C4×D4—1422no—
515C4×D4—1422no—
516C4×D4—1422no—
517C4×D4—1422no—
518C4×D4—1422no—
519C4×D4—1422no—
520C4×D4—1422no—
521C4×D4—1422no—
522C2×C4⋊C4—711no—
523C2×C4⋊C4—711no—
524C2×C4⋊C4—711no—
525C2×C4⋊C4—1422no—
526C2×C4⋊C4—1422no—
527C2×C4⋊C4C4×D7111yescharacteristic, complemented
528C2×C22⋊C4—714no—
529C2×C22⋊C4—7116no—
530C2×C22⋊C4—711no—
531C2×C22⋊C4—711no—
532C2×C22⋊C4—711no—
533C2×C22⋊C4—711no—
534C2×C22⋊C4—711no—
535C2×C22⋊C4—711no—
536C2×C22⋊C4—1422no—
537C2×C22⋊C4—1422no—
538C2×C22⋊C4—1422no—
539C2×C22⋊C4—1422no—
540C2×C22⋊C4—1428no—
541C2×C22⋊C4—1424no—
542C2×C22⋊C4C4×D7111yescharacteristic, complemented
543C2×C22⋊C4C22×D7111yescharacteristic
544C2×C22⋊C4C22×D7114yes—
545C2×C42—22no—
546C2×C42—2848no—
547C2×C42—711no—
548C2×C42—711no—
549C2×C42—711no—
550C2×C42—1421no—
551C2×C42—1421no—
552C2×C42—1421no—
553C2×C42—1421no—
554C2×C42—1424no—
555C2×C42—1422no—
556C2×C42C4×D7111yescharacteristic, complemented
557#99—718no—
558#99—7116no—
559#99C4×D7118yesdirect product factor
560#95—22no—
561#95—1424no—
562#95—1422no—
563C24—2842no—
564C24—2842no—
565C24—2842no—
566C24—2842no—
567C24—714no—
568C24—711no—
569C24—712no—
570C24—714no—
571C24—711no—
572C24—714no—
573C24—711no—
574C24—712no—
575C24—1421no—
576C24—1421no—
577C24—1422no—
578C24C2×C4×D7111yescharacteristic
579C24C23×D7111yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—714no—
583C2×D4—714no—
584C2×D4—714no—
585C2×D4—1422no—
586C2×D4—1422no—
587C2×D4—14216no—
588C2×D4—14216no—
589C2×D4—1422no—
590C2×D4—1422no—
591C2×D4—1422no—
592C2×D4—1422no—
593C2×D4C2×C4×D7114yes—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—2842no—
600C22×C4—2844no—
601C22×C4—2842no—
602C22×C4—2848no—
603C22×C4—2848no—
604C22×C4—2844no—
605C22×C4—2844no—
606C22×C4—2844no—
607C22×C4—2844no—
608C22×C4—2842no—
609C22×C4—2842no—
610C22×C4—2842no—
611C22×C4—2844no—
612C22×C4—2842no—
613C22×C4—2842no—
614C22×C4—2844no—
615C22×C4—2842no—
616C22×C4—2842no—
617C22×C4—711no—
618C22×C4—712no—
619C22×C4—712no—
620C22×C4—712no—
621C22×C4—712no—
622C22×C4—711no—
623C22×C4—711no—
624C22×C4—711no—
625C22×C4—711no—
626C22×C4—711no—
627C22×C4—712no—
628C22×C4—714no—
629C22×C4—711no—
630C22×C4—711no—
631C22×C4—712no—
632C22×C4—712no—
633C22×C4—711no—
634C22×C4—712no—
635C22×C4—1421no—
636C22×C4—1421no—
637C22×C4—1421no—
638C22×C4—1421no—
639C22×C4—14216no—
640C22×C4—1421no—
641C22×C4—1421no—
642C22×C4—1428no—
643C22×C4—1424no—
644C22×C4—1421no—
645C22×C4—1421no—
646C22×C4—1422no—
647C22×C4—1421no—
648C22×C4—1421no—
649C22×C4—1424no—
650C22×C4—1421no—
651C22×C4—1421no—
652C22×C4C2×C4×D7111yescharacteristic
653C22×C4C2×C4×D7111yescharacteristic
654C22×C4C2×C4×D7111yescharacteristic
655C22×C4C2×C4×D7111yescharacteristic
656C22×C4C2×C4×D7111yescharacteristic
657C22×C4D4×D7112yes—
658C22×C4D4×D7112yes—
659C4⋊C4—22no—
660C4⋊C4—1422no—
661C4⋊C4—1422no—
662C4⋊C4—1422no—
663C22⋊C4—22no—
664C22⋊C4—24no—
665C22⋊C4—22no—
666C22⋊C4—718no—
667C22⋊C4—1422no—
668C22⋊C4—14216no—
669C22⋊C4—1422no—
670C22⋊C4—1422no—
671C22⋊C4—1422no—
672C22⋊C4—1422no—
673C22⋊C4—1424no—
674C22⋊C4—1422no—
675C22⋊C4C2×C4×D7118yescomplemented
676C42—21no—
677C42—21no—
678C42—44no—
679C42—2844no—
680C42—2848no—
681C42—1421no—
682C42—1421no—
683C42—1421no—
684C42—1421no—
685C42—1421no—
686C42—1421no—
687C23—21no—
688C23—21no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—2841no—
694C23—2841no—
695C23—2842no—
696C23—2841no—
697C23—2842no—
698C23—2841no—
699C23—2842no—
700C23—2842no—
701C23—2842no—
702C23—2848no—
703C23—2842no—
704C23—2848no—
705C23—2848no—
706C23—2848no—
707C23—712no—
708C23—712no—
709C23—718no—
710C23—712no—
711C23—711no—
712C23—712no—
713C23—712no—
714C23—711no—
715C23—712no—
716C23—718no—
717C23—1424no—
718C23—1424no—
719C23—1424no—
720C23—1422no—
721C23—1424no—
722C23—1422no—
723C23—1421no—
724C23—1421no—
725C23C42×D7112yescomplemented
726C23C22×C4×D7111yescharacteristic
727C23C22×C4×D7112yes—
728C23C2×D4×D7112yes—
729C23#41×D7112yes—
730D4—28no—
731D4—1428no—
732D4—1428no—
733D4—1428no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—28no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—2842no—
750C2×C4—2842no—
751C2×C4—2842no—
752C2×C4—2842no—
753C2×C4—2842no—
754C2×C4—2842no—
755C2×C4—2842no—
756C2×C4—28432no—
757C2×C4—2842no—
758C2×C4—2842no—
759C2×C4—2842no—
760C2×C4—2844no—
761C2×C4—2844no—
762C2×C4—2842no—
763C2×C4—2842no—
764C2×C4—2842no—
765C2×C4—2841no—
766C2×C4—2841no—
767C2×C4—2842no—
768C2×C4—2841no—
769C2×C4—711no—
770C2×C4—714no—
771C2×C4—712no—
772C2×C4—711no—
773C2×C4—712no—
774C2×C4—1422no—
775C2×C4—1424no—
776C2×C4—1422no—
777C2×C4—1424no—
778C2×C4—1424no—
779C2×C4—1424no—
780C2×C4—1421no—
781C2×C4—1421no—
782C2×C4—1428no—
783C2×C4—1424no—
784C2×C4—1422no—
785C2×C4—1421no—
786C2×C4—1421no—
787C2×C4—1422no—
788C2×C4—1424no—
789C2×C4C42×D7112yescomplemented
790C2×C4C22⋊C4×D7111yescharacteristic
791C2×C4C22⋊C4×D7112yes—
792C2×C4C22⋊C4×D7111yescharacteristic
793C22—22no—
794C22—21no—
795C22—22no—
796C22—21no—
797C22—22no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—41no—
803C22—41no—
804C22—2842no—
805C22—2842no—
806C22—2848no—
807C22—2842no—
808C22—2842no—
809C22—2848no—
810C22—2848no—
811C22—2841no—
812C22—2841no—
813C22—712no—
814C22—712no—
815C22—712no—
816C22—712no—
817C22—714no—
818C22—14216no—
819C22—1424no—
820C22—1424no—
821C22—1422no—
822C22—1421no—
823C22—1422no—
824C22—1421no—
825C22—1422no—
826C22C2×C42×D7111yescharacteristic
827C22C2×C22⋊C4×D7111yescharacteristic
828C22#117×D7111yescharacteristic
829C22C4×D4×D7114yes—
830C4—21no—
831C4—22no—
832C4—22no—
833C4—48no—
834C4—41no—
835C4—41no—
836C4—2848no—
837C4—2841no—
838C4—2841no—
839C4—712no—
840C4—1421no—
841C4—1422no—
842C4—1422no—
843C4#99×D7112yesdirect product factor
844C2—24no—
845C2—21no—
846C2—21no—
847C2—42no—
848C2—2842no—
849C2—714no—
850C2—1422no—
851C2—1424no—
852C2C4×C22⋊C4×D7111yescharacteristic
853C2C2×#99×D7111yescharacteristic
854C2#410×D7111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D71
commutatorC22×C71C22×C42
FrattiniC24C23×D71
FittingC4×#99×C71C2
socleC22×C71C22×C22⋊C4
prime radicalC22×D4×D71C22
cosocleC24×C71C24
hypercenterC4×#99D71
hypocenterC71C2×C4×#99
LCSG ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C4×C22⋊C4×D71C2semidirect
4. #99×Dic71C2semidirect
5. C4×#14556042C2semidirect
6. C4×#14556043C2semidirect
7. #22588127C2semidirect
8. #342×D71C2semidirect
9. C4×#99×C71C2semidirect
11. C23×C4×D71C4semidirect
13. C2×C4×D284C4semidirect
15. C2×#14556090C4semidirect
16. C2×C4×C22⋊D71C4semidirect
18. C2×(C22⋊D71)⋊C4C4semidirect
24. C2×C4⋊C4×D71C4semidirect
25. C2×C22⋊C4×D71C4semidirect
29. C2×C42×D71C4semidirect
32. #99×D71C4direct (N × H)
33. C22⋊C4×Dic71C22semidirect
35. C4×C22⋊Dic71C22semidirect
38. #17985766C22semidirect
39. #17985765C22semidirect
42. C4×C22⋊C4×C71C22semidirect
43. #342×C71C22semidirect
53. C23×Dic71C2×C4semidirect
69. C22×C4×D71C2×C4semidirect
70. C22×C4×D71C2×C4semidirect
89. C2×C4⋊Dic71C2×C4semidirect
90. C2×Dic71⋊C4C2×C4semidirect
91. C2×Dic71⋊C4C2×C4semidirect
94. C2×C22⋊Dic71C2×C4semidirect
100. C2×(C2×D71)⋊C4C2×C4semidirect
101. C2×(C2×D71)⋊C4C2×C4semidirect
107. C22⋊C4×D71C2×C4semidirect
110. C2×C4×Dic71C2×C4semidirect
111. C2×C4×Dic71C2×C4semidirect
112. C2×C4×Dic71C2×C4semidirect
118. #14556043C2×C4semidirect
119. #14556042C2×C4semidirect
123. C23×C4×C71C2×C4semidirect
127. C2×C4⋊C4×C71C2×C4semidirect
128. C2×C22⋊C4×C71C2×C4semidirect
132. C2×C42×C71C2×C4semidirect
133. #99×C71C2×C4semidirect
142. C23×D71C42semidirect
152. C2×D284C42semidirect
157. C2×C22⋊D71C42semidirect
203. C2×C4×D71C42semidirect
220. C22⋊Dic71C22×C4semidirect
255. C22⋊C4×C71C22×C4semidirect
265. C23×C71C2×C42semidirect
294. C22×D71C2×C42semidirect
318. C2×C4×C71C2×C42semidirect
339. C2×Dic71C2×C42semidirect
364. C4×D71#99direct (N × H)
408. C4×C71C2×#99semidirect
415. Dic71C2×#99semidirect
427. D71C4×#99direct (N × H)
435. C4×#99D71direct (N × H)
437. C71C2×C4×#99semidirect
467. C4×C22⋊C4C2×D71semidirect
471. #342C2×D71semidirect
504. C23×C4C4×D71semidirect
527. C2×C4⋊C4C4×D71semidirect
542. C2×C22⋊C4C4×D71semidirect
556. C2×C42C4×D71semidirect
559. #99C4×D71direct (N × H)
675. C22⋊C4C2×C4×D71semidirect
725. C23C42×D71semidirect
789. C2×C4C42×D71semidirect
843. C4#99×D71direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×D4×D712
C2×#99×D712
C4×C22⋊C4×D712
#99×Dic712
C4×#145560422
C4×#145560432
#225881272
#342×D712
C4×#99×C712
C2×C4×#9971